There are many ways to determine a position of a device. For example, some existing positioning systems such as global positioning systems (GPS) use satellites, while other systems such as collaborative positioning systems determine the position of the device based on crowd-sourced data (e.g., previously received positioned observations). Beacon positions, also estimated from crowd-sourced observation data, are used to estimate the position of the device that requests position information based on an observed list of beacons (e.g., a beacon fingerprint). The complexity and accuracy of the estimated device position depends in part on the data describing the beacons selected as input to the positioning system.
For example, it is difficult to accurately estimate a beacon radius, such as when there are few observations for a particular beacon. The estimated beacon radius may not reflect the actual beacon radius for a given confidence level (e.g., 90%, 95%, etc.). When one of the positioning systems attempts to infer a device position and device error radius associated with the inferred device position using such potentially inaccurate beacon radius estimates, the resulting device error radius may also be inaccurate.